No exceptional precision of exceptional point sensors

TL;DR

This paper demonstrates that sensors operating at exceptional points do not offer superior precision over traditional sensors, as their quantum-limited signal-to-noise ratio scales linearly with perturbation, contradicting previous claims.

Contribution

The study clarifies that exceptional point sensors do not have enhanced sensitivity due to the behavior of eigenvectors and frequency splitting near EPs, challenging prior assumptions.

Findings

Quantum-limited SNR is proportional to perturbation at EPs.

Complex frequency splitting does not improve sensor precision.

Eigenvector behavior explains the lack of enhanced sensitivity.

Abstract

Recently, sensors with resonances at exceptional points (EPs) have been suggested to have a vastly improved sensitivity due to the extraordinary scaling of the complex frequency splitting of the $n$ initially degenerate modes with the $n$-th root of the perturbation. We show here that the resulting quantum-limited signal to noise at EPs is proportional to the perturbation, and comparable to other sensors, thus providing the same precision. The complex frequency splitting close to EPs is therefore not suited to estimate the precision of EP sensors. The underlying reason of this counter-intuitive result is that the mode fields, described by the eigenvectors, are equal for all modes at the EP, and are strongly changing with the perturbation.